基于1阶剪切变形理论（FSDT）和Hamilton原理，利用狄拉克函数描述加筋，推导夹芯复合材料加筋板在真空中的自由振动控制方程；进一步假设浸没于水中的夹芯复合材料加筋板为薄板，根据流固耦合面上的法向加速度连续条件，对横向自由振动方程进行重构，得到整体结构在水中的控制方程。考虑四边简支边界条件，采用双傅里叶级数求解方程，并与文献及数值结果进行对比，验证了本文方法的有效性。进一步研究了加筋位置和数量、面板厚度及芯层厚度变化对夹芯复合材料加筋板自由振动的影响，为工程实际的结构优化设计提供参考。
Free vibration control equation of the sandwich composite stiffened plate in vacuum is derived which is based on the first-order shear deformation theory (FSDT) and the Hamilton principle and Dirac function is used to describe the stiffener. The submerged sandwich composite stiffened plate is regarded as a thin plate underwater, and according to the continuous condition of normal acceleration on the fluid-solid coupling surface, the lateral free vibration equation is reconstructed to obtain the governing equation of the overall structure in water. The double Fourier series is used to solve the free vibration of the simply supported sandwich composite stiffened plate, and comparing the results with the numerical simulation results. The conclusions verify the effectiveness of the solution method. The influence of stiffening position, quantity and thickness changes of plate and core layer on the free vibration of the sandwich composite stiffened plate is further studied, which provides a reference for the optimal design of the actual project.
2022,44(11): 12-21 收稿日期：2021-11-18
DOI：10.3404/j.issn.1672-7649.2022.11.003
分类号：TB332
基金项目：国家自然科学基金资助项目(51779098)
作者简介：耿佳傲(1996-)，男，硕士研究生，研究方向为船舶振动与噪声
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